Hemispherical resonator gyroscopes have been around for many years and are considered the highest performing vibratory rotation sensors on the market. A typical hemispherical resonator gyroscope includes a fused silica hemisphere that is driven by a forcer electrode and sensed using a separate set of pickoff electrodes. The hemispherical resonator gyroscope may measure rotation rates or rotation angles through the rotational-vibrational coupling (e.g., Coriolis coupling) between structural modes of the gyroscope. One of the modes, designated the drive mode, is initially made to oscillate at high levels of velocity. Rotation induced Coriolis force then couples motion from the first mode into a secondary structural mode with a magnitude proportional to the magnitude of the input rotation. The most commonly used vibrational modes used in hemispherical resonator gyroscopes are the two cos 2θ modes, named for their mode shape.
The ring down time is a figure of merit of every hemispherical resonator gyroscope and is commonly designated by the symbol τ. The ring down time may be considered the amplitude decay constant of the hemispherical resonator of the gyroscope if all external forces are removed and the hemisphere is allowed to freely oscillate. The ring down time may also quantify the amount of effort required to maintain the oscillation pattern of the hemispherical resonator, where a hemispherical resonator with a larger ring down time requires less effort. The ring down time is proportional to the equivalent mass (m) and damping coefficient (b) of the hemispherical resonator where τ=2 m/b. As is understood by those skilled in the art, mathematically, the equivalent mass of a hemispherical resonator gyroscope can of a be thought of as a series of point masses located at the points of maximum velocity or maximum deflection for the two mode shapes where the rest of the hemisphere is assumed to be massless. In a hemisphere, the equivalent mass is roughly equal to one third the total mass of the hemisphere. To increase the ring down time, τ, the equivalent mass of the hemispherical resonator of the gyroscope may be made larger, typically through increasing the hemisphere diameter. However, there are many applications that call for a fixed size hemisphere or a micro-scale gyroscope where increasing the size of the hemisphere is not feasible or practical.
For example, some applications (e.g., personal or mobile applications) may constrain or restrict the form factor of the hemisphere to be no more than a particular diameter. In addition, some applications (e.g., military or outdoor applications) may constrain or restrict the power supplied to the gyroscope. For example, in a power loss environment, the ring down time may dictate how the long the gyroscope will continue to operate without being driven. Thus, increasing the ring down time of a hemispherical resonator gyroscope is typically at odds with maintaining the form factor of the gyroscope.